Face-to-face , first term, 30 hours of theory and 22,5 hours of exercises.

First term
Friday from 14:00 to 16:00 at 109 Marais 301

The course and tutorials are taught in French; the reference book is in English.

General aim:
To introduce to the way of reasoning of statistical inference and to the fundamental methods of statistical analysis. These methods are useful in every scientific field where random and/or experimental aspects occur (human, technical, medical and natural sciences). The course will especially develop the tools and models useful for economics and management sciences.

Specific aims:
At the end of the “in depth statistics” course, the students should be able:
- to understand the mechanism of statistical inference;
- to correctly model an inference problem;
- to solve and treat simple and standard problems of statistical inference;
- to master the fundamental concepts of the estimation theory and hypothesis tests;
- to apply these concepts to non-standard models;
- to solve and treat classical statistical problems, regression analysis, variance analysis, and adjustment tests.

For the Bachelor : Business Engineering :

None

This course, as well as the “probabilities” course, is based on the following book (available at the reprography service):
W. Mendenhall, D. Wackerly and R. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, 7th edition, 2008.
- chapters 1 to 7 constitute the subject matter of “Probabilities” in BAC 1;
- chapters 7 to 14 constitute the subject matter of “Extensive Statistics” in BAC 2.

This course presents the following chapters:
- Chapter 7: Sampling and « central-limit » theorem;
- Chapter 8: Point and interval estimation: fundamental elements;
- Chapter 9: Estimation theory;
- Chapter 10: Hypothesis tests;
- Chapter 11: Regression model and least squares adjustment (including matrix notation);
- Chapter 12: Introduction to experimental plans (comparison of two means: paired or independent samples);
- Chapter 13: One-criterion Variance analysis;
- Chapter 14: Analysis of categorical data (Chi-square tests: goodness-of-fit test and test of independence).

Lecture and tutorials

The assessment is a closed book written examination:
- the examination questions will be selected among the exercises and examples of the handbook (the list of relevant exercises will be given during the tutorials);
- these questions will be completed by other, more theoretical, questions;
- the students will have at their disposal a form with the main discrete and continuous probability principles studied in class and their main characteristics (moments, ...) ;
- they will also have a general form including the main useful probability and statistical formulas;
- the useful statistical tables will also be available.
Active assistance at lectures and tutorials is highly recommended. Regular work (including solving exercises) is compulsory from the first week on.

The written examination takes place during the two last exam sessions, in the following way: the complete examination lasts three hours. During the first part (first hour), the student will be assessed on his understanding of the course, requiring personal reflection on the whole subject matter. The two following hours will be devoted to exercise solving. The first part counts for 1/3 of the final mark, and the second part counts for the remaining 2/3 of the final mark.

The students will be entitled to use the form mentioned above, the statistical tables and their calculator (not alphanumerical).

- Wackerly D. D., Mendenhall W and R.L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, 7th ed., 2008.

- Mendenhall W, Beaver R. J. and B. M. Beaver, Introduction to Probability and Statistics, 13th édition. Brooks/Coles, USA, 2009.

- Mood A.M., Graybill F.A. and D.C. Boes, Introduction to the Theory of Statistics, Mc Graw Hill Ed., 1974.

- Rohatgi V. K. and A. M. Md. Ehsanes Saleh, Introduction to probability and Statistics, Wiley Series in Probability and Statistics, 2d Ed., 2001.

- Mendenhall W and T. Sincich, Statistics for Engineering and the Sciences, Pearson Prentice Hall, 5th ed., 2007.

- Larsen R. J. and M.L. Marx, An Introduction to Mathematical Statistics and its Applications, Pearson International Edition, 4th ed., 2006.

- The course is compulsory for the students in Management Engineering and for the students who have taken the “Quantitative methods” orientation in the bachelor in economics and management.
- The course is recommended for students looking for an in depth training in statistics.
- This course is part of a logical progression in statistical training. It is normally preceded by the “probabilities” course in BAC 1 and followed by the “multivariate statistics and econometrics” course in BAC 3.
- The course is to be avoided by students experiencing difficulties in mathematics.